We don't believe in God because we have no proof that he exists. You can twist logic and play silly word games from now until Cairo hosts the winter Olympics, but that is all there is to it.

That the Bible says there is a God is not proof in any manner or form whatsoever that there is in fact a God. Of course we've heard of God, but we've seen not one shred of evidence to suggest that he is more than an enduring (sadly) figment of mankind's imagination. Like the tooth fairy or the Easter bunny.